The scattering diagram \(\mathcal {D}_Q\)  can be defined as the set of decorated rays
\(\lbrace \mathcal {R}_Q(\gamma ) : \gamma \in \Gamma _+\rbrace \) 
equipped with the automorphism \(\mathcal {U}_\theta (\gamma )\) 
at each point. The wall-crossing formula for DT invariants ensures
that \(\mathcal {D}_Q\)  is consistent in the following sense [1]}: for any
generic closed path \(\mathcal {P}\colon t\in [1,0]\rightarrow {R}^{Q_0}\)  (where generic means that
the intersection of \(\mathcal {P}\)  with a ray \(\mathcal {R}(\gamma _i)\)  at \(t=t_i\)  is transverse
and does not meet any cone of codimension larger than one),
the ordered product of automorphisms associated to each intersection is trivial
\(\prod _i \mathcal {U}_{\theta (t_i)} (\gamma _i)^{\epsilon _i} = 1\ ,\quad \epsilon _i=\operatorname{sign}\left( \frac{\mathrm {d}\theta }{\mathrm {d}t}, \gamma _i\right)\) 
